Lower bounds for topological complexity

New Lower Bounds for the Topological Complexity of Aspherical Spaces

We show that the topological complexity of an aspherical space X is bounded below by the cohomological dimension of the direct product A×B, whenever A and B are subgroups of π1(X) whose conjugates intersect trivially. For instance, this assumption is satisfied whenever A and B are complementary subgroups of π1(X). This gives computable lower bounds for the topological complexity of many groups ...

Some Lower Bounds for Estrada Index

Lower complexity bounds for interpolation algorithms

We introduce and discuss a new computational model for Hermite–Lagrange interpolation by nonlinear classes of polynomial interpolants. We distinguish between an interpolation problem and an algorithm that solves it. Our model includes also coalescence phenomena and captures a large variety of known Lagrange-Hermite interpolation problems and algorithms. Like in traditional Hermite–Lagrange inte...

Lower Bounds for Quantum Communication Complexity

We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower bounds developed by Raz [30] to the quantum case. Applying this method we give an exponential separation between bounded error quantum communication complexity a...

Inferring Lower Bounds for Runtime Complexity

We present the first approach to deduce lower bounds for innermost runtime complexity of term rewrite systems (TRSs) automatically. Inferring lower runtime bounds is useful to detect bugs and to complement existing techniques that compute upper complexity bounds. The key idea of our approach is to generate suitable families of rewrite sequences of a TRS and to find a relation between the length...